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Simplifying 5k + 31 = -2 + -7(3 + -2k) Reorder the terms: 31 + 5k = -2 + -7(3 + -2k) 31 + 5k = -2 + (3 * -7 + -2k * -7) 31 + 5k = -2 + (-21 + 14k) Combine like terms: -2 + -21 = -23 31 + 5k = -23 + 14k Solving 31 + 5k = -23 + 14k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-14k' to each side of the equation. 31 + 5k + -14k = -23 + 14k + -14k Combine like terms: 5k + -14k = -9k 31 + -9k = -23 + 14k + -14k Combine like terms: 14k + -14k = 0 31 + -9k = -23 + 0 31 + -9k = -23 Add '-31' to each side of the equation. 31 + -31 + -9k = -23 + -31 Combine like terms: 31 + -31 = 0 0 + -9k = -23 + -31 -9k = -23 + -31 Combine like terms: -23 + -31 = -54 -9k = -54 Divide each side by '-9'. k = 6 Simplifying k = 6
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